%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:18:57 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 10:49:24 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable
% 0.07/0.38
% 0.07/0.39 % SZS output start Proof
% 0.07/0.40 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.07/0.40 Axiom 2 (xLEy): less_equal(x, y) = true.
% 0.07/0.40 Axiom 3 (yLEz): less_equal(y, z) = true.
% 0.07/0.40 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.40 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.07/0.40 Axiom 6 (closure): quotient(X, Y, divide(X, Y)) = true.
% 0.07/0.40 Axiom 7 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 0.07/0.40 Axiom 8 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 0.07/0.40 Axiom 9 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.07/0.40 Axiom 10 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 0.07/0.40
% 0.07/0.40 Goal 1 (prove_transitivity_of_less_equal): less_equal(x, z) = true.
% 0.07/0.40 Proof:
% 0.07/0.40 less_equal(x, z)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(true, true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 6 (closure) R->L }
% 0.07/0.40 ifeq(quotient(x, z, divide(x, z)), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(less_equal(divide(x, z), zero), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(true, true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 6 (closure) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, divide(divide(x, z), zero)), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(less_equal(divide(divide(x, z), zero), zero), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(x, z), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 6 (closure) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(x, z, divide(x, z)), true, less_equal(divide(divide(x, z), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(true, true, ifeq(quotient(x, z, divide(x, z)), true, less_equal(divide(divide(x, z), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 7 (quotient_less_equal) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(ifeq(less_equal(y, z), true, quotient(y, z, zero), true), true, ifeq(quotient(x, z, divide(x, z)), true, less_equal(divide(divide(x, z), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 3 (yLEz) }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(ifeq(true, true, quotient(y, z, zero), true), true, ifeq(quotient(x, z, divide(x, z)), true, less_equal(divide(divide(x, z), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, less_equal(divide(divide(x, z), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(true, true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 7 (quotient_less_equal) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(ifeq(less_equal(x, y), true, quotient(x, y, zero), true), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 2 (xLEy) }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(ifeq(true, true, quotient(x, y, zero), true), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.40 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(true, true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.40 = { by axiom 7 (quotient_less_equal) R->L }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(ifeq(less_equal(zero, z), true, quotient(zero, z, zero), true), true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 1 (zero_is_smallest) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(ifeq(true, true, quotient(zero, z, zero), true), true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(zero, z, zero), true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 4 (ifeq_axiom) R->L }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(true, true, ifeq(quotient(zero, z, zero), true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 6 (closure) R->L }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(ifeq(quotient(divide(x, z), zero, divide(divide(x, z), zero)), true, ifeq(quotient(zero, z, zero), true, ifeq(quotient(y, z, zero), true, ifeq(quotient(x, z, divide(x, z)), true, ifeq(quotient(x, y, zero), true, less_equal(divide(divide(x, z), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 10 (quotient_property) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero)), divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 5 (ifeq_axiom) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(less_equal(zero, divide(divide(x, z), zero)), true, zero, divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 1 (zero_is_smallest) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, ifeq2(true, true, zero, divide(divide(x, z), zero))), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 5 (ifeq_axiom) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(ifeq(quotient(divide(x, z), zero, zero), true, less_equal(divide(x, z), zero), true), true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 8 (less_equal_quotient) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(true, true, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z)), divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 5 (ifeq_axiom) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(less_equal(zero, divide(x, z)), true, zero, divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 1 (zero_is_smallest) }
% 0.07/0.41 ifeq(quotient(x, z, ifeq2(true, true, zero, divide(x, z))), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 5 (ifeq_axiom) }
% 0.07/0.41 ifeq(quotient(x, z, zero), true, less_equal(x, z), true)
% 0.07/0.41 = { by axiom 8 (less_equal_quotient) }
% 0.07/0.41 true
% 0.07/0.41 % SZS output end Proof
% 0.07/0.41
% 0.07/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------